A fully loaded boeing aircraft has a mass of 5.4 × 10⁵ kg. Its total wing area is 500 m ². It is in level flight with a speed of 1080 km/h. If the density of air ρ is 1.2 kg m ⁻³, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ( g = 10 m/s²) (a) 16 (b) 8 (c) 6 (d) 10

Answer: (d). Level flight: lift = mg ⇒ Δ P = mg/A = 5.4×10⁶500 = 1.08×10⁴ Pa Bernoulli: Δ P = 1/2ρ(vu² - vl²) ≈ ρ v Δ v, with v = 1080 km/h = 300 m/s Δ v = 1.08×10⁴1.2 × 300 = 30 m/s (Δ v)/(v) = 30/300 = 0.1 = 10% So the answer is (d) 10.

A fully loaded boeing aircraft has a mass of 5.4 × 10⁵ kg. Its total… | JEE Main 2023 (29 Jan, Shift 2)

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Applications of Bernoulli's Theorem

A fully loaded boeing aircraft has a mass of $5.4 \times 10^{5}$ kg. Its total wing area is 500 m $^{2}$ . It is in level flight with a speed of 1080 km/h. If the density of air $\rho$ is 1.2 kg m $^{-3}$ , the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ( $g = 10\text{ m/s}^2$ )

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Answer: (d)

Level flight: lift $= mg \Rightarrow \Delta P = \frac{mg}{A} = \frac{5.4\times10^{6}}{500} = 1.08\times10^{4}\text{ Pa}$
Bernoulli: $\Delta P = \frac{1}{2}\rho(v_u^2 - v_l^2) \approx \rho v\,\Delta v$ , with $v = 1080\text{ km/h} = 300\text{ m/s}$
$\Delta v = \frac{1.08\times10^{4}}{1.2 \times 300} = 30\text{ m/s}$
$\frac{\Delta v}{v} = \frac{30}{300} = 0.1 = 10\%$
So the answer is (d) 10.

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